Coherent optical vibration sensors have been investigated for use in numerous applications including strain measurements, equipment diagnostics, medical imaging, and seismic sensing. Various techniques have been utilized to observe surface motion including heterodyne laser Doppler vibrometry (e.g., U.S. Pat. No. 4,834,111 to Khanna et al.) for observation of surface velocity in the axial dimension of the interrogation beam, shearography (e.g., U.S. Pat. No. 5,011,280 to Hung) for observation of the gradient of displacement in two dimensions, electronic speckle pattern interferometry (e.g., U.S. Pat. No. 4,018,531 to Leendertz) for dynamic out of plane contour observation, and heterodyne digital image correlation for out-of-plane displacement and rotation (U.S. Pat. No. 9,651,477 to Libbey et al.). Techniques to observe the image and Fourier planes simultaneously to measure in-plane translation and out-of-plane rotation have been demonstrated using direct detection and holographic techniques. (See, e.g., Kelly, D. P., Hennelly, B. M., & Sheridan, J. T. (2005), “Magnitude and direction of motion with speckle correlation and the optical fractional Fourier transform,” Applied optics, 44(14), 2720-2727; and Bhaduri, B., Quan, C., Tay, C. J., & Sjodahl, M. (2010), “Simultaneous measurement of translation and tilt using digital speckle photography,” Applied optics, 49(18), 3573-3579.)
The techniques listed are generally used for observation of one or two degrees of freedom. Variations using multiple coherent beams (e.g., U.S. Pat. No. 7,242,481 B2 to Shpantzer et al.) have been used to observe three degrees of freedom, or three-dimensional deformations. (See, also, Rajshekhar, G., Gorthi, S. S., & Rastogi, P. (2011), “Simultaneous measurement of in-plane and out-of-plane displacement derivatives using dual-wavelength digital holographic interferometry,” Applied optics, 50(34), H16-H21; Alvarez, A. S., Manuel, H., Santoyo, F. M., & Anaya, T. S. (2014), “Strain determination in bone sections with simultaneous 3D digital holographic interferometry,” Optics and Lasers in Engineering, 57, 101-108; and Saucedo-A, T., De la Torre-Ibarra, M. H., Santoyo, F. M., & Moreno, I. (2010), “Digital holographic interferometer using simultaneously three lasers and a single monochrome sensor for 3D displacement measurements,” Optics express, 18(19), 19867-19875.) It is of interest to observe in-plane and out-of-plane components of motion using a single interrogation beam.